I might as well, since I'm idle at work today. By the way Bushwhacker, I did the Lone Star trail at Castle Mountain, Alberta, as mentioned by Lady Salina, not the Starr trail at Stowe. But I'll use Starr as my example.
I guess you have to download Google Earth to get all the tools, as opposed to using Google Maps. Enter Stowe vt as your location (I love watching Google Earth fly you across the country). Pan northwest to Mt Mansfield and zoom in on the Nose. Use the pan and tilt tools at the top to get a good look at the steepness. The elevation at your cursor is shown at the bottom. There used to be some problems with these elevations especially on mountain peaks, but it's much better now.
Click on the ruler tool at the top, and select feet instead of miles. Click at the top of the slope you want to measure, and note the elevation. Then draw a line to the bottom of the slope and note the elevation there. The difference is your vertical drop. The Ruler popup will show a distance which is the horizontal length between your end points, i.e. what it would be on a map. The angle can be got from the tangent, which is the vertical divided by the horizontal. Here's a trig table in case you don't have a scientific calculator: http://math2.org/math/trig/tables.htm
For the steepest pitch at the top of Starr I get a top elevation of 3290 and a bottom elevation of 2940, for a vertical of 350 feet. The popup shows a base length of 556 feet. So the tangent is 0.6295, and the angle is 32.2 degrees. If you want the whole trail down to the Lookout liftline, use the Path tool instead of Line so you can go around bends. The vertical is 1096 feet over a length of 2304 for a tangent of 0.476, which is an angle of 25.4 degrees.